On the Complexity of Modulo-q Arguments and the Chevalley - Warning Theorem
We study the search problem class PPA_q defined as a modulo-q analog of the well-known polynomial parity argument class PPA introduced by Papadimitriou (JCSS 1994). Our first result shows that this class can be characterized in terms of PPA_p for prime p. Our main result is to establish that an explicit version of a search problem associated to the Chevalley - Warning theorem is complete for PPA_p for prime p. This problem is natural in that it does not explicitly involve circuits as part of the input. It is the first such complete problem for PPA_p when p ≥ 3. Finally we discuss connections between Chevalley-Warning theorem and the well-studied short integer solution problem and survey the structural properties of PPA_q.
LIPIcs-CCC-2020-19.pdf
publisher
openaccess
CC BY
894.94 KB
Adobe PDF
e7601c77470f59df58f8ddfe1be7f8d5